Casimir-like Effect In Bose-Einstein Condensation

Casimir first predicted that, in the electromagnetic vacuum, there is an attractive force due to zero-point quantum fluctuations between two closely perfect conductive plates. This force is called Casimir force and its value is.Since it was predicted in 1948, the Casimir effect has played an important role in the physics field. It is an interdisciplinary subject. It plays an important role in a variety of fields of physics such as Quantum Electrodynamics, Condensed Matter Physics, Atomic and Molecular Physics, Gravitation and Cosmology, and Mathematical Physics. In 1924, Bose and Einstein predicted that if the de Broglie wavelength larger than the average wavelength between the particles, there will be a phase transition. A number of particles will occupy the ground-state and this transition is called Bose-Einstein Condensation (BEC). It is one of the greatest scientific findings in the 21st century. At present, there is about more than 30 labs have realized the BEC.In the paper, I review the present research and experiment progress of the Casimir effect and Bose-Einstein Condensation briefly. On the foundation of other researchers'work, I further study the Casimir-like effect of absolute zero-temperature dilute Bose-Einstein Condensation. I obtain a precise expression of the Casimir-like force, then calculate and discuss it. We not only obtain others' findings, namely the influence of linear part of the Bogoliubov dispersion relation on the Casimir-like force, but aslo calculate the influence of non-linear part. It indicates that the influence of linear part is more important than the non-linear part. In the calculaton, we do not introduce any ultraviolet cut-off parameter or function, and solve the limited analysis expression. It not only provides a new calculation method to research the Casimir force, but also provides a theory proof for measurement of the Casimir-like force.